Nuclear magnetic resonance imaging or zeugmatography employs the physical phenomenon of nuclear magnetic resonance to provide detection of the spatial distribution of certain nuclear spins at characteristic frequencies in the radiofrequency range. This spatial distribution provides information as to the state of corresponding areas of a sample, and provides resolution down to an order of about 1 mm in humans. Zeugmatography has been found to be particularly applicable to biological systems such as man because of its non-invasive and apparently hazard-free nature.
A review of NMR imaging techniques and applications appears in an article by R. M. Bottomley in Rev. Sci. Instrum. 53(9), September 1982, pages 1319 to 1336.
Briefly stated, the resonance frequency, known as the Larmor frequency, is related to the magnetic field which is applied to the sample by the following relationship: EQU .omega..sub.o =-.gamma.H.sub.o ( 1)
where
.omega.o is the Larmor frequency, PA1 Ho is the component of the applied magnetic field along a principal field axis z as experienced by the nucleus of the atom whose spin is detected, and PA1 .gamma. is the gyromagnetic ratio characteristic of each nuclear species. PA1 G is the applied field gradient, PA1 .delta.x is the required degree of linear spatial resolution demanded of the system, and PA1 1/T.sub.2 * is the width of the frequency signal from the sample in the absence of the applied gradient.
By labelling the spins at different locations in the sample with differing Larmor frequencies it is possible to map the spin densities and relaxation times T1 and T2 in regions of the sample.
The major effort in the design of NMR imaging systems is directed to providing a magnetic field Ho which is space dependent in a known and predictable manner within the sample. This is normally achieved by superimposing a linearly varying field on the magnetic field existing within the sample by passing electric currents through suitably shaped gradient producing coils which surround the sample.
It may be understood from a consideration of equation (1) above, that reconstruction of the NMR image is based on the assumption that the known superimposed linear variation in the magnetic field is the only source of spatial magnetic field variation. In practice, however, this is not correct, since magnetic field inhomogeneities may appear as a result of external magnetic sources, inherent design and construction limitations and as the result of variations in magnetic susceptibility in the sample.
Conventionally, the problem of magnetic field inhomogeneities is overcome by a brute force technique, wherein the superimposed field gradients are caused to be so large as to dominate the inhomogeneities and thus render them inconsequential. Such a condition may be expressed by the following inequality: EQU .gamma.G.delta.x.gtoreq.1/T.sub.2 * (2)
where
The frequency width 1/T.sub.2 * can be expressed as: EQU 1/T.sub.2 *=1/T.sub.2 +.DELTA..omega..sub.(inh) ( 3)
where 1/T.sub.2 is the intrinsic linewidth of the nuclear absorption signal and .DELTA..omega..sub.(inh) is the broadening of the frequency band caused by the magnetic field inhomogeneities. Normally .DELTA..omega..sub.(inh) is much larger than 1/T.sub.2, typically by more than an order of magnitude.
The provision of large gradients for the purpose of overwhelming the magnetic field inhomogeneities involves very significant expenses in the construction and operation of the large magnets that are required. A correspondingly large investment in infrastructure is also required. The results produced nevertheless have a resolution limitation determined by the signal to noise characteristics thereof.